Skip to Main content Skip to Navigation
Theses

Stabilité d’ondes périodiques, schéma numérique pour le chimiotactisme

Abstract : This thesis is organized around two aspects of the study of partial differentialequations. In a first part, we study the stability of periodic solutions for conservationlaws. First, we prove asymptotic L1-stability of periodic solutions of scalarinhomogeneous conservation laws. Then, we show a result on structural stability ofroll-waves. More precisely, we prove that periodic solutions of a hyperbolic systemwithout viscosity are the limits of the solutions of the problem with viscosity, as theviscous term tends to 0. In a second part, we study a system of partial differentialequations derived from biology: the model of Patlak-Keller-Segel in dimension 2, describingthe phenomena of chemotaxis. For this model, we construct a finite-volumescheme, which approaches the solution while keeping some properties of the system:positivity, conservation of mass, energy estimate.
Document type :
Theses
Complete list of metadata

Cited literature [74 references]  Display  Hide  Download

https://tel.archives-ouvertes.fr/tel-00845883
Contributor : ABES STAR :  Contact
Submitted on : Thursday, July 18, 2013 - 10:12:12 AM
Last modification on : Saturday, September 24, 2022 - 3:36:05 PM
Long-term archiving on: : Saturday, October 19, 2013 - 4:16:10 AM

File

TH2010_Le_-_Blanc_-_ValA_rie.p...
Version validated by the jury (STAR)

Identifiers

  • HAL Id : tel-00845883, version 1

Citation

Valérie Le Blanc. Stabilité d’ondes périodiques, schéma numérique pour le chimiotactisme. Mathématiques générales [math.GM]. Université Claude Bernard - Lyon I, 2010. Français. ⟨NNT : 2010LYO10091⟩. ⟨tel-00845883⟩

Share

Metrics

Record views

262

Files downloads

238